The more water i pour into sink, the more more slower it will drain. Something it blocking in one of the pipes. I had this problem a year ago.I removed the pvc pipe in kitchen to see if anything was blocked, but there was nothing. So it is probably the pipes behind the wall. Is there a way to fix this?

I'd try a plunger, just not the same one already used on the toilet. The quick spin might work, but it shouldn't be a long run to the main drain pipe, in which case a 1/4" cable won't be effective with the clog. If you are able to see the drain pipes from the basement, you can look for a clean-out on the main. And if you have a dishwasher connected to the sink, it might hinder the effectiveness of the plunger.. If all else fails, there is always chemicals, which I only like to use as a last resort.